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Alexandr E. Krasnok, Pavel A. Belov, Andrey E. Miroshnichenko, Arseniy I. Kuznetsov,Boris S. Luk’yanchuk, Yuri S. Kivshar

Content

1 All-dielectric optical nanoantennas 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1 Optical magnetism based on dielectric nanoparticles . . . . . . . . . . . 5

1.2 Huygens optical elements and Yagi—Uda nanoantennas based on dielectric

nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

(i) General concept . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

(ii) Experimental verification of dielectric Yagi-Uda nanoantenna . . 13

1.3 All–dielectric superdirective optical nanoantenna . . . . . . . . . . . . . 15

(i) Concept of all–dielectric superdirective optical nanoantennas . . . 17

(ii) Steering of light at the nanoscale . . . . . . . . . . . . . . . . . . 22

(iii) Experimental verification of superdirective optical nanoantenna . 23

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

References 25

1

1 All-dielectric optical nanoantennas

Introduction

Antennas are important elements of wireless information communication technologies, along

with sources of electromagnetic radiations and their detectors. One can say that antennas

are at the heart of modern radio and microwave frequency communications technologies.

They are at the front-ends of satellites, cell-phones, laptops and other communicating

devices. In radio engineering, antennas refer to devices converting electric and magnetic

currents into radio propagating waves and, vice versa, radio waves to currents. Recently,

the concept of antennas have been extended to the optical frequency domain [1–9]

Fig. 1.1 – The basic principles of nanoantennaoperation (exemplified by a nanodipole). Near field

(a) or waveguide mode (b) transformation intofreely propagating optical radiation; Panels (c, d)illustrate a reception regime. The configuration of

feeding via a plasmonic waveguide is of greatimportance for practical applications of

nanoantennas, especially for the development ofwireless communication systems at the nanometer

level, i.e., for future photonic chips. [8]

as a result of the development of a new

branch of physics emerged known as nanooptics,

which studies the transmission and reception of

optical signals by submicron and even nanometer-

sized objects.

For nanooptics it is important to efficiently

detect and direct the transmitting signals for

optical information between nanoelements. The

sources and detectors of radiation in nanooptics

are nanoelements themselves, their clusters,

and even individual molecules (atoms, ions).

Nanoobjects functioning as antennas must exhibit

high radiation efficiency and directivity.

Nanoantennas, similar to the radiofrequency

antennas, are usually divided into two types,

transmitting and receiving (see Fig. 1.1). Figure

1.1a schematically shows the interaction between

a nanoantenna and the near field of an quantum

emitter. In this case, the nanoantenna transforms

the near field into freely propagating optical radiation, i.e. it is a transmitting nanoantenna. Figure

1.1c illustrates the operation of a receiving nanoantenna that converts incident radiation into a strongly

confined near field.

2

The energy is usually delivered to a microwave antenna through a waveguide. Such an antenna

converts waveguide modes to freely propagating radiation. In the case of optical antennas with their

sufficiently small optical size, the waveguide mode must have the subwavelength cross section attainable

by using so-called plasmonic waveguides. This type of nanoantenna feeding is depicted schematically

in Fig. 1.1b. According to the reciprocity principle, such a nanoantenna is also capable of transforming

incident radiation to plasmonic waveguide modes (see Fig. 1.1d).

Fig. 1.2 – Plethora of nanoantennas application inmodern science. [8]

Thus, the transmitting antenna converts a

strongly confined field in the optical frequency

range created by a certain (weakly emitting or

almost non emitting) source into optical radiation

(see Fig. 1.1a,b). Conversely, the receiving

nanoantenna is a device efficiently converting

incident light (optical frequency radiation) into

a strongly confined field (see Fig. 1.1c,d),

where an electromagnetic field is concentrated

in a small region compared to the wavelength

of light. Such fields are characterized by a

spatial spectrum consisting mostly of evanescent

waves. The confinement region may be of

subwavelength dimension, leading to a strongly

confined near field. The energy of this field

contains contributions from stored and non

radiated energy. However, an important particular case of nanoantennas is a device converting

optical radiation into waveguide modes, and vice versa, as shown in Fig. 1.1c,d. In this case, the

subwavelength dimension is characterized by the transverse cross section of the strongly confined

field region. The longitudinal size of this region (along the waveguide axis) may be optically large,

and the electromagnetic energy of the strongly confined field is referred to as expanding. The

feeding configuration with a plasmonic waveguide is of great importance for practical applications

of nanoantennas, especially for the development of wireless communication systems at the nanometer

level, i.e., for future fully optical integrated circuits.

Fig. 1.3 – Main types of plasmonic nanoantennas. [8]

3

Nanoantennas are the most promising area of research in the modern nanooptics due to their

ability to bridge the size and impedance mismatch between nanoemitters and free space radiation, as

well as manipulate light on the scale smaller than the wavelength of light. Bearing in mind the great

variety of sources and detectors of strongly confined optical fields (groups of atoms and molecules,

luminescent and fluorescent cells, e.g., viruses and bacteria, sometimes individual molecules, quantum

dots, and quantum wires), it is safe to say that the areas of practical applications of nanoantennas in

the near future will be commensurate with that of their classical analogs.

At present, nanoantennas are used in near-field microscopy and high-resolution biomedical sensors;

their application for hyperthermal therapy of skin neoplasms is a matter of the foreseeable future. There

are some other potential applications of nanoantennas (see Fig. 1.2) that we believe to be equally

promising, including solar cells [10], molecular and biomedical sensors [11], optical communication

[12], and optical tweezers [13]. The variety of applications allows us to argue that the concept of

nanoantennas presents a unique example of the penetration of new physics into various spheres of

human activity.

Thus far, optical antennas have primarily been constructed from metallic materials, which

support plasmonic resonances. The main types of plasmonic nanoantennas which have been realized

experimentally are presented in Fig. 1.3. Different types of plasmonic nanoantennas are designed to

perform various tasks. For example dipole nanoantennas [8, 9, 14–16] demonstrate high coefficient of

electric field localization, while bowtie nanoantennas [8, 9, 13, 17–24] are broadband; Yagi-Uda type

nanoantennas exhibit high directivity which is very useful for optical wireless communications on an

optical chip [3, 8, 9, 12, 25–35]. However, despite of a number of advantages of plasmonic nanoantennas

associated with their small size and strong localization of the electric field, such nanoantennas have

large dissipative losses resulting in low radiation efficiency.

To overcome such limitations, we propose a new type of nanoantennas based on dielectric

nanoparticles with a high index dielectric constant [8, 9, 36–44], for example Huygens optical elements

and Yagi-Uda nanoantennas [see par.(1.2)]. Such all-dielectric optical nanoantennas will have low

dissipative losses with enhanced magnetic response in the visible. The concept of optical magnetism

based on dielectric nanoparticles is presented in the next section. The key for such novel functionalities

of high index dielectric nanophotonic elements is the ability of subwavelength dielectric nanoparticles to

support simultaneously both electric and magnetic resonances, which can be controlled independently.

This type of nanoantennas has several unique features such as low optical losses at the nanoscale

and superdirectivity. The concept of all-dielectric nanoantennas has been developed in our original

papers [8, 9, 40–42,45, 46] and also summarized below.

Furthermore all-dielectric nanoantennas allow us achieve the superdirectivity effect.

Superdirectivity as a physical concept can be found in textbooks on antennas, however all so far

proposed superdirective antennas are not reliably reproducible. More specifically, all previous attempts

to achieve superdirectivity of antennas were based on discrete arrays of radiating dipoles with a

rather cumbersome distribution of radiating currents over the array. This approach resulted in intrinsic

drawbacks of known superdirective arrays - ultra-narrowfrequency range, high dissipation, and extreme

sensitivity to any disturbance, etc. As a result, no single superdirective antenna was demonstrated up to

now. In the context of nanoantennas, which originated from radio frequency antennas a few years ago,

4

Fig. 1.4 – Schematic representation of electric and magnetic field distribution inside a metallicsplit-ring resonator (a) and a high-refractive index dielectric nanoparticle (b) at magnetic resonance

wavelength. [47]

superdirectivity has never been discussed. However, superdirectivity would be a very desirable feature in

nanophotonics with numerous useful applications. Here we describe [see par.(1.3)] the superdirectivity

effect in a very simple, elegant, and practical way for a nanoparticle with a notch. This approach is able

to shape higher-harmonics of the radiation field in such a way that not only superdirectivity of this

nanoantennas becomes possible but also a strong subwavelength sensitivity of the radiation pattern to

the location of the emitter can be easily realized.

1.1 Optical magnetism based on dielectric nanoparticles

It is well known that a pair of oscillating electric charges of opposite signs, know as an oscillating

electric dipole, produces electromagnetic radiation at the oscillations frequency [48]. Although, distinct

“magnetic charges”, or monopoles, have not been observed so far, magnetic dipoles are very common

sources of magnetic field in nature. The field of the magnetic dipole is usually calculated as the limit of

a current loop shrinking to a point. Its profile is equivalent to the one of an electric dipole considering

that the electric and magnetic fields are exchanged. The most common example of a magnetic dipole

radiation is an electromagnetic wave produced by an excited metal split-ring resonator (SRR), which

is a basic constituting element of metamaterials (see Fig. 1.4a) [49–57]. The real currents excited by

external electromagnetic radiation and running inside the SRR produce a transverse oscillating up and

down magnetic field in the center of the ring, which simulates an oscillating magnetic dipole. The major

interest of these artificial systems is due to their ability to response to a magnetic component of incoming

radiation and thus to have a non-unity or even negative magnetic permeability (µ) at optical frequencies,

which does not exist in nature. This provides possibilities to design unusual material properties such as

negative refraction [49–57], cloaking [58, 59], or superlensing [60]. The SRR concept works very well

for gigahertz [55–57], terahertz [61,62] and even near-infrared (few hundreds THz) [63–65] frequencies.

However, for shorter wavelengths and in particular for visible spectral range this concept fails due to

increasing losses and technological difficulties to fabricate smaller and smaller constituting split-ring

elements [64,66]. Several other designs based on metal nanostructures have been proposed to shift the

magnetic resonance wavelength to the visible spectral range [49,50]. However, all of them are suffering

from losses inherent to metals at visible frequencies.

An alternative approach to achieve strong magnetic response with low losses is to use nanoparticles

made of high-refractive index dielectric materials [53, 67]. As it follows from the exact Mie solution of

5

light scattering by a spherical particle, there is a particular parameter range where strong magnetic

dipole resonance can be achieved. Remarkably, for the refractive indices above a certain value there

is a well-established hierarchy of magnetic and electric resonances. In contrast to plasmonic particles

the first resonance of dielectric nanoparticles is a magnetic dipole resonance, and takes place when the

wavelength of light inside the particle equals to the diameter λ/ns ≃ 2Rs, where λ is a wavelength in a

free space, Rs and ns are the radius and refractive index of spherical particle. Under this condition the

polarization of the electric field is anti-parallel at opposite boundaries of the sphere, which gives rise

to strong coupling to circulation displacement currents while magnetic field oscillates up and down in

the middle (see Fig. 1.4b).

Below in this section we present the experimental results demonstrating [47] that spherical silicon

nanoparticles with sizes in the range from 100 nm to 200 nm have strong magnetic dipole response in

the visible spectral range. The scattered “magnetic” light by these nanoparticles is so strong that it can

be easily seen under a dark-field optical microscope. The wavelength of this magnetic resonance can be

tuned throughout the whole visible spectral range from violet to red by just changing the nanoparticle

size.

In article [47] we have chosen silicon (Si) as a material which has high refractive index in

the visible spectral range (above 3.8 at 633 nm) on one side and still almost no dissipation losses

on the other. Silicon nanorods have attracted considerable attention during the last few years due

to their ability to change their visible color with the size [68]. This effect appears due to excitation

of particular modes inside the cylindrical silicon nanoresonators. Moreover, recent theoretical work

predicted that spherical silicon nanoparticles with sizes of a few/several hundred nanometers should

have both strong magnetic and electric dipole resonances in the visible and near-IR spectral range

[69, 70]. To fabricate the silicon nanoparticles we have used the laser ablation technique, which is an

efficient method to produce nanoparticles of various materials and sizes [71]. Nanoparticles produced

by the ablation method can be localized on a substrate and measured separately from each other using

single nanoparticle spectroscopy.

Dark-field microscopic image of a silicon sample ablated by a focused femtosecond laser beam is

shown in Fig. 1.5a. It shines by all the colours of the rainbow from violet to red. To clarify the origin of

this strong scattering we selected some nanoobjects shining with different colours on the sample (see

Fig. 1.5 – Dark-field microscope (a) and top-view scanning electron microscope (SEM) (b) images ofthe same area on a silicon wafer ablated by a femtosecond laser. Microscope image is inverted in

horizontal direction relative to that of the SEM. Selected nanoparticles are marked by correspondingnumbers 1 to 6 in both figures. [47]

6

Fig. 1.5a) and measured their scattering spectra by single nanoparticle dark-field spectroscopy. Then,

the same sample area was characterized by scanning electron microscopy and the selected nanoobjects

providing different colours have been identified (see Fig. 1.5b, the dark-field microscope image is inverted

in horizontal direction relative to that of the SEM). The results of this comparative analysis of the same

nanoobjects by dark-field optical microscopy, dark-field scattering spectroscopy, and scanning electron

Fig. 1.6 – Close-view dark-field microscope (i) and SEM (ii) images of the single nanoparticlesselected in Fig. 1.5. Figures (a) to (f) correspond to nanoparticles 1 to 6 from Fig. 1.5 respectively.(iii) Experimental dark-field scattering spectra of the nanoparticles. (iv) Theoretical scattering and

extinction spectra calculated by Mie theory for spherical silicon nanoparticles of different sizes in freespace. Corresponding nanoparticle sizes are defined from the SEM images (ii) and noted in each

figure. [47]

7

microscopy are presented in Fig. 1.6. As it can be seen from the SEM images the observed colours

are provided by silicon nanoparticles of almost perfect spherical shape and varied sizes. This makes it

possible to analyze scattering properties of these nanoparticles in the frames of Mie theory [72] and

identify the nature of optical resonances observed in our spectral measurements. The bottom panels

(iv) in Fig. 1.6 represent a total extinction cross-section calculated using Mie theory [72] for silicon

nanoparticles of different sizes (the calculations were done in free space). In these calculations, the size

of the nanoparticles in each figure was chosen to be similar to the size defined from each corresponding

SEM image (ii). It can be seen that there is a clear correlation between the experimental (iii) and

theoretical spectra (iv) both in the number and position of the observed resonances. This makes it

obvious that Mie theory describes more or less accurately our experimental results.

One of the main advantages of the analytical Mie solution compared to other computational

methods is its ability to split the observed spectra into separate contributions of different multipole

modes and have a clear picture of the field distribution inside the particle at each resonance maximum.

This analysis was done for each particle size in Fig. 1.6 and corresponding multipole contributions

were identified (see notations in the experimental and theoretical spectra). According to this analysis

the first strongest resonance of these nanoparticles appearing in the longer wavelength part of the

spectrum corresponds to magnetic dipole response (md). Electric field inside the particle at this

resonance wavelength has a ring shape while magnetic field oscillates in the particle center. Magnetic

dipole resonance is the only peak observed for the smallest nanoparticles (see Fig. 1.6a). At increased

nanoparticle size (see Fig. 1.6b,c) electric dipole (ed) resonance also appears at the blue part of the

spectra, while magnetic dipole shifts to the red. For relatively small nanoparticles, the observed colour

is mostly defined by the strongest resonance peak and changes from blue to green, yellow, and red when

magnetic resonance wavelength shifts from 480 nm to 700 nm (see Fig. 1.6a–d). So, we can conclude

that the beautiful colours observed in the dark field microscope (see Fig. 1.5a) correspond to magnetic

dipole scattering of the silicon nanoparticles, “magnetic light”. Further increase of the nanoparticle size

leads to the shift of magnetic and electric dipole resonances further to the red and infra-red frequencies,

while higher multipole modes such as magnetic and electric quadrupoles appear in the blue part of the

spectra (see Fig. 1.6d–f).

Some differences between experimental and theoretical spectra observed in Fig. 1.6 can be

attributed to the presence of silicon substrate, which is not taken into account in our simple Mie theory

solution. We should also mention that very similar results have been published almost simultaneously

by a different group of authors [73] who demonstrated magnetic and electric dipole resonances of silicon

particles in red and near-IR spectral range.

Recently we have also experimentally demonstrated for the first time directional light scattering by

spherical silicon nanoparticles in the visible spectral range [74]. These unique scattering properties arise

due to simultaneous excitation and mutual interference of magnetic and electric dipole resonances inside

a single nanosphere. This phenomenon is similar to a known since long time Kerker-type scattering

predicted in [75] for hypothetical magneto-dielectric nanoparticles but never observed experimentally.

Directivity of the far-field radiation pattern can be controlled by changing light wavelength and the

nanoparticle size. Forward-to-backward scattering ratio above 6 was experimentally obtained at visible

wavelengths. Similar directional light scattering by spherical ceramic particles in GHz [76] and GaAs

8

Fig. 1.7 – (A) Huygens element consisting of a single silicon nanoparticle and point-like dipole sourceseparated by a distance Gds = 90 nm (between dipole and sphere surface). The radius of the siliconnanoparticle is Rs = 70 nm. (B) Dielectric optical Yagi-Uda nanoantenna, consisting of the reflectorof the radius Rr = 75 nm, and smaller director of the radii Rd = 70 nm. The dipole source is placedequally from the reflector and the first director surfaces at the distance G. The separation between

surfaces of the neighbouring directors is also equal to G. [45]

nanodisks in the visible [77] has also been published almost simultaneously by different groups of

authors. These unique optical properties of high-refractive index dielectric nanostructures constitute

the background for our approach to all-dielectric nanoantennas, which will be discussed in detail below.

1.2 Huygens optical elements and Yagi—Uda nanoantennas

based on dielectric nanoparticles

Recently, it was suggested [8, 9, 40–42, 45, 46] a novel type of optical nanoantennas made of

all-dielectric elements. Moreover, we argue that, since the source of electromagnetic radiation is

applied externally, dielectric nanoantennas can be considered as the best alternative to their metallic

counterparts. First, dielectric materials exhibit low loss at the optical frequencies. Second, as was

suggested earlier, nanoparticles made of high-permittivity dielectrics may support both electric and

magnetic resonant modes. This feature may greatly expand the applicability of optical nanoantennas

for, e.g. for detection of magnetic dipole transitions of molecules [78]. In our study we concentrate on

nanoparticles made of silicon. The real part of the permittivity of the silicon in the visible spectral

range is about 16 [79], while the imaginary part is up to two orders of magnitude smaller than that of

nobel metals (silver and gold).

(i) General concept

The mentioned above properties of dielectric nanoparticles allow us to realize optical Huygens

source [80] consisting of a point-like electric dipole operating at the magnetic resonance of a

dielectric nanosphere (see Fig.1.7A). Such a structure exhibits high directivity with vanishing backward

scattering and polarization independence, being attractive for efficient and compact designs of optical

nanoantennas.

We start our analysis by considering a radiation pattern of two ideal coupled electric and magnetic

dipoles. A single point-like dipole source generates the electric far-field of the following form

9

Ep =k2

4πǫ0rexp(ikr) [p− n(n · p)] , (1.1)

where p is the electric dipole, k = ω/c is the wavenumber, n is the scattered direction, and r is the

distance from the dipole source. The radiation pattern σ = limr→∞

4πr2|Ep|2 in the plane of the dipole

n × p = 0 is proportional to the standard figure-eight profile, σ|| ∝ | cosα|2, where α is the scattered

angle. In the plane orthogonal to the dipole (n · p = 0) the radiation pattern remains constant and

angle independent, σ⊥ ∝ const. Thus, the total radiation pattern of a single dipole emitter is a torus

which radiates equally in the opposite directions. If we now place, in addition to the electric dipole, an

orthogonal magnetic dipole located at the same point, the situation changes dramatically. The magnetic

dipole m generates the electric far-field of the form

Em = −

√

µ0

ǫ0

k2

4rπexp(ikr) (n×m) . (1.2)

Thus, the total electric field is a sum of two contributions from both electric and magnetic dipoles

Etotal = Ep+Em. By assuming that the magnetic dipole is related to the electric dipole via the relation

|m| = |p|/(µ0ǫ0)1/2, which corresponds to an infinitesimally small wavefront of a plane wave often

called a Huygens source [80], the radiation pattern becomes σH ∝ |1 + cosα|2. This radiation pattern

is quite different compared to that of a single electric dipole. It is highly asymmetric with the total

suppression of the radiation in a particular direction, α = π [σH(π) = 0], and a strong enhancement in

the opposite direction, α = 0. The complete three-dimensional radiation pattern resembles a cardioid

or apple-like shape, which is also azimuthally independent. Such a radiation pattern of the Huygens

source is potentially very useful for various nanoantenna applications. However, while electric dipole

sources are widely used in optics, magnetic dipoles are less common.

First, we consider an electric dipole source placed in a close proximity to a dielectric sphere [see

Fig. 1.7(a)]. As was mentioned above, it can be analytically shown that high permittivity dielectric

nanoparticles exhibit strong magnetic resonance in the visible range when the wavelength inside the

nanoparticle equals its diameter λ/ns ≈ 2Rs [81], where nS and Rs are refractive index and radius of

the nanoparticle, respectively. There are many dielectric materials with high enough real part of the

permittivity and very low imaginary part, indicating low dissipative losses. To name just a few, silicon

(Si, ǫ1 = 16), germanium (Ge, ǫ1 = 20), aluminum antimonide (AlSb, ǫ1 = 12), aluminum arsenide

(AlAs, ǫ1 = 10), and other. In our study we concentrate on the nanoparticles made of silicon, which

support strong magnetic resonance in the visible range for the radius varying from 40 nm to 80 nm [69].

For such a small radius compared to the wavelength Rs < λ, the radiation pattern of the silicon

nanoparticle in the far field at the magnetic or electric resonances will resemble that of magnetic or

electric point-like dipole, respectively. Moreover, it is even possible to introduce magnetic αm and

electric αe polarisabilities [69, 72, 82] based on the Mie dipole scattering coefficients b1 and a1:

αe =6πa1i

k3, αm =

6πb1i

k3. (1.3)

Thus, the dielectric nanoparticle excited by the electric dipole source at the magnetic resonance

may result in the total far field radiation pattern which is similar to that of the Huygens source. Similar

radiation patterns can be achieve in light scattering by a magnetic particle when permeability equals

10

Fig. 1.8 – Wavelength dependence of the directivity of two types of all-dielectric nanoantennasconsisting of (a) single dielectric nanoparticle of radius Rd = 70 nm, and (b) Yagi-Uda like design for

the separation distance D = 70 nm. Insert shows 3D radiation pattern diagrams at particularwavelengths. [45]

permittivity µ = ǫ, also known as Kerker’s condition [75]. Our result suggests that even a dielectric

nonmagnetic nanoparticle can support two induced dipoles of equal strength resulting in suppression of

the radiation in the backward direction. Thus, it can be considered as the simplest and efficient optical

nanoantenna with very good directivity.

In general, both polarisabilities αm and αe are nonzero in the optical region [69]. It is known that

for a dipole radiation in the far field the electric and magnetic components should oscillate in phase

to have nonzero energy flow. In the near field the electric and magnetic components oscillate with π/2

phase difference, thus, the averaged Poynting vector vanishes, and a part of energy is stored in the

vicinity of the source. In the intermediate region, the phase between two components varies form π/2

to 0. Placing a nanoparticle close to the dipole source will change the phase difference between two

components, and, thus, will affect the amount of radiation form the near field. In the case of plasmonic

nanoparticles which exhibit electric polarizability only, there is an abrupt phase change from 0 to π

in the vicinity of the localized surface plasmon resonance, which makes it difficult to tune plasmonic

nanoantennas for optimal performance. The dependence of the scattering diagram on the distance

between the electric dipole source and metallic nanoparticle was studied in Ref. [83]. On contrary, in

the case of nanoparticles with both electric and magnetic polarisabilities, it is possible to achieve more

efficient radiation from the near to far field zone, due to subtle phase manipulation. This is exactly the

case of the dielectric nanoparticles.

Any antenna is characterized by two specific properties, directivity (D) and radiation efficiency

(ηrad), defined as [80, 84]

D =4π

PradMax[p(θ, ϕ)], ηrad =

PradPrad + Ploss

, (1.4)

where Prad and Ploss are integrated radiated and absorbed powers, respectively, θ and ϕ are spherical

angles of standard spherical coordinate system, and p(θ, ϕ) is the radiated power in the given direction

θ and/or ϕ. The directivity measures the power density of the antenna radiated in the direction of its

strongest emission, while Radiation Efficiency measures the electrical losses that occur throughout the

antenna at a given wavelength. To calculate these quantities numerically for the structures shown in

Fig. 1.7a, we employ CST Microwave Studio. To get reliable results, we model the electric dipole source

11

by a Discrete Port coupled to two PEC nanoparticles.

In Fig. 1.8(a) we show the dependence of the directivity on wavelength for a single dielectric

nanoparticle excited by a electric dipole source. Two inserts demonstrate 3D angular distribution of

the radiated pattern p(θ, ϕ) corresponding to the local maxima. In this case, the system radiates

predominantly to the forward direction at λ = 590 nm, while in another case, the radiation is

predominantly in the backward direction at λ = 480 nm. In this case, the total electric dipole moment of

the sphere and point-like source and the magnetic dipole moment of the sphere oscillate with the phase

difference arg(αm)−arg(αe) = 1.3rad, resulting in the destructive interference in the forward direction.

At the wavelength λ = 590 nm the total electric and magnetic dipole moments oscillate in phase and

produce Huygens-source-like radiation pattern with the main lobe directed in the forward direction.

By adding more elements to the silicon nanoparticle, we can enhance the performance of all-dielectric

nanoantennas. In particular, we consider a dielectric analogue of the Yagi-Uda design (see Fig.1.7)

consisting of four directors and one reflector. The radii of the directors and the reflector are chosen to

achieve the maximal constructive interference in the forward direction along the array. The optimal

performance of the Yagi-Uda nanoantenna should be expected when the radii of the directors correspond

to the magnetic resonance, and the radius of the reflector correspond to the electric resonance at a given

frequency, with the coupling between the elements taken into account. Our particular design consists

of the directors with radii Rd = 70 nm and the reflector with the radius Rr = 75 nm. In Fig. 1.8(b) we

plot the directivity of all-dielectric Yagi-Uda nanoantenna vs. wavelength with the separation distance

D = 70 nm. Inserts demonstrate the 3D radiation patterns at particular wavelengths. We achieve a

strong maximum at λ = 500 nm. The main lobe is extremely narrow with the beam-width about

40 and negligible backscattering. The maximum does not correspond exactly to either magnetic or

electric resonances of a single dielectric sphere, which implies the importance of the interaction between

constitutive nanoparticles.

As the next step, we study the performance of the all-dielectric nanoantennas for different

separation distances D, and compare it with a plasmonic analogue of the similar geometric design

made of silver nanoparticles. According to the results summarized in Fig. 1.9, the radiation efficiencies

of both types of nanoantennas are nearly the same for larger separation of directors D = 70 nm with

the averaged value 70%. Although dissipation losses of silicon are much smaller than those of silver, the

dielectric particle absorbs the EM energy by the whole spherical volume, while the metallic particles

absorb mostly at the surface. As a result, there is no big difference in the overall performance of these

Fig. 1.9 – Radiation efficiencies of (a) dielectric (Si) and (b) plasmonic (Ag) Yagi-Uda opticalnanoantennas of the same geometrical designs for various values of the separation distance D. [45]

12

Fig. 1.10 – Purcell factor of all-dielectric Yagi-Uda nanoantenna vs wavelength for various values ofthe separation distance D. [45]

two types of nanoantennas for relatively large distances between the elements. However, the difference

becomes very strong for smaller separations. The radiation efficiency of the all-dielectric nanoantenna

is insensitive to the separation distance [see Fig. 1.9 (a)]. On contrary, the radiation efficiency drops

significantly for metallic nanoantennas [see Fig. 1.9 (b)].

Finally, we investigate the modification of the transition rate of a quantum point-like source

placed in the vicinity of dielectric particles. For electric-dipole transitions and in the weak-coupling

regime, the normalised spontaneous decay rate Γ/Γ0, also known as Purcell factor, can be calculated

classically as the ratio of energy dissipation rates of an electric dipole P/P0 [7]. Here, Γ0 and P0

correspond to transition rate of the quantum emitter and energy dissipation rate of the electric dipole

in free space [85]. In the limit of the intrinsic quantum yield of the emitter close to unity, both ratios

become equal to each other Γ/Γ0 = P/P0, which allows us to calculate the Purcell factor in the classical

regime [7]. We have calculated the Purcell factor by using both, numerical and analytical approaches.

Numerically, by using the CST Microwave Studio we calculate the total radiated in the far-field and

dissipated into the particles powers and take the ratio of their sum to the total power radiated by the

electric dipole in free space. Analytically, we employed the generalised multiparticle Mie solution [86]

adapted for the electric dipole excitation [87]. We verified that both approaches produce similar results.

In Fig. 1.10 we show calculated Purcell factor of the all-dielectric Yagi-Uda nanoantenna vs. wavelength

for various separation distances. We observe that, by decreasing the separation between the directors,

the Purcell factor becomes stronger near the magnetic dipole resonance. We can notice that a plasmonic

analogue of the same nanoantenna made of Ag exhibits low Purcell factor less than one. Thus, such

relatively high Purcell factor can be employed for efficient photon extraction from molecules placed

near all-dielectric optical nanoantennas.

(ii) Experimental verification of dielectric Yagi-Uda nanoantenna

There are exist some technological issues to reproduce an object of the nanometer size with a

high accuracy. For this reason we have scaled the dimensions of the proposed optical all-dielectric

Yagi-Uda nanoantenna to the microwave frequency range while keeping all the material parameters

in order to study the microwave analogue of the nanoantenna experimentally. We use the design of

the Yagi-Uda antenna shown in Fig. 1.7b. To mimic the silicon spheres in microwave frequency range,

we employ MgO-TiO2 ceramic which is characterized by dielectric constant of 16 and dielectric loss

13

Fig. 1.11 – Photographs of the all-dielectric Yagi-Uda microwave antenna. (a) Detailed view of theantenna placed in a holder. (b) Antenna placed in an anechoic chamber; the coordinate z is directed

along the vibrator axis; the coordinate y is directed along the antenna axis. [46]

factor of (1.12−1.17)10−4 measured at frequency 9-12 GHz [88]. As a source, we use a half-wavelength

vibrator. We study experimentally both the radiation pattern and directivity of the antenna.

We set the radius of the reflector equal to Rr = 5 mm. The frequencies of the electric and magnetic

Mie resonances of the sphere calculated with the help of Eq. (1.3) are 10.2 GHz and 7 GHz, respectively.

The radius of the directors is Rd = 4 mm. In this case, the frequencies of the electric and magnetic Mie

resonances are 12.5 GHz and 9 GHz. As a source, we model a half-wavelength vibrator with the total

length of Lv = 19.8 mm and diameter of Dv = 2.2 mm. The distances between the reflector, directors,

and vibrator have been adjusted by numerical simulations. We achieve an effective suppression of the

back and minor lobes, and the narrow major lobe (of about 40) of the antenna when the distance

between the director’s surface as well as the distance between vibrator center and the first director

surface are 1.5 mm; the distance between the surface of the reflector and vibrator centre is 1.1 mm.

Figures 1.11(a,b) show the photographs of the fabricated all-dielectric Yagi-Uda antenna. The

reflector and directors are made of MgO-TiO2 ceramic with accuracy of ±0.05 mm. To fasten together

the elements of the antenna and vibrator, we use a special holder made of a thin dielectric substrate with

dielectric permittivity close to 1 [being shown in Fig. 1.11(a)]. Styrofoam material with the dielectric

permittivity of 1 is used to fix the antenna in the azimuthal-rotation unit [see Fig. 1.11(b)]. To feed

the vibrator, we employ a coaxial cable that is connected to an Agilent PNA E8362C vector network

analyzer.

Any antenna is characterized by the total directivity (1.4). Sometimes it is not possible to

determine the value of the total directivity experimentally due to difficulties to measure the total

radiated power Prad. In this case, it is convenient to use directivity in the planes where electric field

E and magnetic field H oscillate in the far field. For our coordinates the directivity in the evaluation

plane (E-plane) and the azimuthal plane (H-plane) can be expressed as:

DE =2πMax[p(θ)]∫ 2π

0p(θ)dθ

∣

∣

∣

∣

∣

ϕ=0

, DH =2πMax[p(ϕ)]∫ 2π

0p(ϕ)dϕ

∣

∣

∣

∣

∣

θ=π/2

. (1.5)

Equations (1.5) are multiplied by 2π because of the integration in the denominator is performed only

for one coordinate while the second coordinate is fixed.

To extract the antenna directivity in the E- and H-planes from the experimental data, we measure

14

the radiated power by the antenna in the frequency range from 10 GHz to 12 GHz with a step of

50 MHz. Then, by employing Eq. (1.5) we calculate the directivity at each frequency. The results

are presented in Fig. 1.12a. To estimate the performance of the all-dielectric Yagi-Uda antenna at

microwaves, we simulate numerically the antenna’s response by employing the CST Microwave Studio.

We observe excellent agreement between numerical results of Fig. 1.12b and measured experimental

data. However, we notice a small frequency shift of the measured directivity (approx. 2%) in comparison

with the numerical results. This discrepancies can be explained by the effect of the antenna holders in

the experiment, not included into the numerical simulation.

The antenna radiation patterns in the far field (at the distance ≃ 3 m) are measured in an anechoic

chamber by a horn antenna and rotating table. The measured radiation patterns of the antenna in E-

and H-planes at the frequency 10.7 GHz are shown in Fig. 1.13. The measured characteristics agree

very well with the numerical results. A small disagreement can be explained by the presence of the

antenna holder which influence was not taken into account in our numerical simulations.

1.3 All–dielectric superdirective optical nanoantenna

For optical wireless circuits on a chip, nanoantennas are required to be both highly directive

and compact [12, 89–91]. In nanophotonics, directivity has been achieved for arrayed plasmonic

antennas utilizing the Yagi-Uda design [37, 84, 90, 92, 93], large dielectric spheres [94], and metascreen

antennas [95]. Though individual elements of these arrays are optically small, the overall size of the

radiating systems is larger than the radiation wavelength λ. In addition, small plasmonic nanoantennas

possess weak directivity close to the directivity of a point dipole [90, 96, 97].

As was discussed above, it was suggested theoretically and experimentally to employ magnetic

resonances of high-index dielectric nanoparticles for enhancing the nanoantenna directivity [8,9,37,40–

42,45,46,98]. High-permittivity nanoparticles can have nearly resonant balanced electric and magnetic

dipole responses. This balance of the electric and magnetic dipoles oscillating with the same phase

allows the practical realization of the Huygens source, an elementary emitting system with a cardioid

pattern [37, 44, 46, 80] and with the directivity larger than 3.5. Importantly, a possibility to excite

magnetic resonances leads to the improved nanoantenna directional properties without a significant

Fig. 1.12 – (a )Experimentally measured and (b) numerically calculated antenna’s directivity in bothE- and H-planes. [46]

15

Fig. 1.13 – Radiation pattern of the antenna in (a) E-plane and (b) H-plane at the frequency 10.7GHz. Solid lines show the result of numerical simulations in CST; the crosses correspond to the

experimental data. [46]

increase of its size.

Superdirectivity has been already discussed for radio-frequency antennas, and it is defined as

directivity of an electrically small radiating system that significantly exceeds (at least in 3 times)

directivity of an electric dipole [80, 99, 100]. In that sense, the Huygens source is not superdirective.

In the antenna literature, superdirectivity is claimed to be achievable only in antenna arrays by the

price of ultimately narrow frequency range and by employing very precise phase shifters (see, e.g.,

Ref. [80,99,100]). Therefore, superdirective antennas, though very desirable for many applications such

as space communications and radioastronomy, were never demonstrated and implemented for practical

applications.

Superdirectivity was predicted theoretically for an antenna system [95] where some phase shifts

were required between radiating elements to achieve complex shapes of the elements of a radiating

system which operates as an antenna array. In this paper, we employ the properties of subwavelength

particles excited by an inhomogeneous field with higher-order magnetic multipoles. We consider a

subwavelength dielectric nanoantenna (with the size of 0.4 wavelength) with a notch resonator excited

by a point-like emitter located in the notch. The notch transforms the energy of the generated magneto-

dipole Mie resonance into high-order multipole moments, where the magnetic multipoles dominate. This

system is resonantly scattering i.e. it is very different from dielectric lenses and usual dielectric cavities

which are large compared to the wavelength. Another important feature of the notched resonator is

its huge sensitivity of the radiation direction to a spatial position of the emitter. This property leads

to a strong beam steering effect and subwavelength sensitivity of the radiation direction to the source

location. The proposed design of superdirective nanoantennas may also be useful for collecting single-

source radiation, monitoring quantum objects states, and nanoscale microscopy. In order to achieve

superdirectivity, we should generate subwavelength spatial oscillations of the radiating currents [80,99,

100]. Then, near fields of the antenna become strongly inhomogeneous, and the near-field zone expands

farther than that of a point dipole. The effective antenna aperture can be defined as S = Dmaxλ2/(4π),

where the maximum of directivity Dmax = 4πPmax/Ptot, λ is the wavelength in free space in our

case, Pmax and Ptot are respectively the maximum power in the direction of the radiation pattern

and the total radiation power. By normalizing the effective aperture S by the geometric aperture for a

16

spherical antenna S0 = πR2s, we obtain the definition of superdirectivity [80, 99]:

Sn =Dmaxλ

2

4π2R2s

≫ 1 (1.6)

Practically, the value Sn = 4 . . . 5 is sufficient for superdirectivity of a sphere. In this work,

maximum of 6.5 for Sn is predicted theoretically for the optical frequency range, and the value of 5.9

is demonstrated experimentally for the microwave frequency range.

(i) Concept of all–dielectric superdirective optical nanoantennas

Here we demonstrate a possibility to create a superdirective nanoantenna without hypothetic

metamaterials and plasmonic arrays. We consider a silicon nanoparticle, taking into account the

frequency dispersion of the dielectric permittivity [79]. The radius of the silicon sphere is equal in our

example to Rs = 90 nm. For a simple sphere under rather homogeneous (e.g. plane-wave) excitation,

only electric and magnetic dipoles can be resonantly excited while the contribution of higher-order

multipoles is negligible in the visible [37]. Making a notch in the sphere breaks the symmetry and

increases the contribution of higher-order multipoles into scattering even if the sphere is still excited

homogeneously. Further, placing a nanoemitter (e.g. a quantum dot) inside the notch, as shown in

Fig. 1.14 we create the conditions for the resonant excitation of multipoles: the field exciting the

resonator is now spatially very non-uniform as well as the field of a set of multipoles. In principle, the

notched particle operating as a nanoantenna can be performed by different semiconductor materials and

have various shapes – spherical, ellipsoidal, cubic, conical, as well as the notch. However, in this work,

the particle is a silicon sphere and the notch has the shape of a hemisphere with a radius Rn < Rs.

The emitter is modeled as a point-like dipole and it is shown in Fig. 1.14 by a red arrow.

It is important to mention that our approach is seemingly close to the idea of references [101,102]

where a small notch on a surface of a semiconductor microlaser was used to achieve higher emission

directivity by modifying the field distribution inside the resonator [103]. An important difference

between those earlier studies and our work is that the design discussed earlier is not optically small and

Fig. 1.14 – (A) Geometry of an all-dielectric superdirective nanoantenna excited by a point-likedipole. (B) Concept of the beam steering effect at the nanoscale.

17

the directive emission is not related to superdirectivity. In our case, the nanoparticle is much smaller

than the wavelength, and our design allows superdirectivity. For the same reason our nanoantenna is

not dielectric [104,105] or Luneburg [106,107] lenses. For example, immersion lenses [108–111] are the

smallest from known dielectric lenses, characterized by the large size 1-2 µm in optical frequency range.

The working methodology of such lenses is to collect a radiation by large geometric aperture S, while

Sn ≃ 1. Our approach demonstrates that the subwavelength system, with small geometric aperture, can

have high directing power because of an increase of the effective aperture. Moreover, there are articles

(see. references [85, 112]) where the transition rates of atoms inside and outside big dielectric spheres

with low dielectric constant (approximately 2), were studied.

First, we consider a particle without a notch but excited inhomogeneously by an emitter point.

To study the problem numerically, we employed the simulation software CST Microwave Studio. Image

Fig. 1.15A shows the dependence of the maximum directivity Dmax on the position of the source in the

case of a sphere Rs = 90 nm without a notch, at the wavelength λ = 455 nm (blue curve with crosses).

This dependence has the maximum (Dmax = 7.1) when the emitter is placed inside the particle at the

distance 20 nm from its surface. The analysis shows that in this case the electric field distribution inside

a particle corresponds to the noticeable excitation of higher-order multipole modes not achievable with

the homogeneous excitation.

Furthermore, the amplitudes of high-order multipoles are significantly enhanced with a small

notch around the emitter, as it is shown in Fig. 1.14. This geometry transforms it into a resonator

with high-order multipole moments. In this example the center of the notch is on the nanosphere’s

surface. The optimal radius of the notch (for maximal directivity) is Rn = 40 nm. In Fig. 1.15A the

extrapolation red curve with circles, corresponding to simulation results, shows the maximal directivity

versus the location of the emitter at the wavelength 455 nm. The Fig. 1.15B shows the directivity versus

λ with and without a notch, it exhibits a maximum of 10 for the directivity at 455 nm. The inset shows

the three-dimensional radiation pattern of the structure at λ =455 nm. This pattern has an angular

width (at the level of 3 dB) of the main lobe equal to 40. This value of directivity corresponds to the

normalized effective aperture Sn = 6.5.

Fig. 1.15 – (A) Maximum of directivity depending on the position of the emitter (λ = 455 nm) in thecase of a sphere with and without notch. Vertical dashed line marks the particle radius centered atthe coordinate system. (B) Directivity dependence on the radiation wavelength. The inset shows

three-dimensional radiation pattern of the structure (Rs = 90 nm and Rn = 40 nm).

18

Fig. 1.16 – Distribution of (A) absolute values and (B) phases of the electric field (C and D formagnetic field, respectively) of the all-dielectric superdirective nanoantenna with source in the center

of notch, at the wavelength λ = 455 nm. (E) Dependence of the radiation pattern of all-dielectricsuperdirective nanoantenna on the number of taken into account multipoles. Dipole like source

located along the z axis.

Figures Fig. 1.16A and B show the distribution of the absolute values and phases of the internal

electric field in the vicinity of the nanoantenna. Electric and magnetic fields inside the particle are

strongly inhomogeneous at λ =455 nm i.e. in the regime of the maximal directivity. In this regime,

the internal area where the electric field oscillates with approximately the same phase turns out to

be maximal. This area is located near the back side of the spherical particle, as can be seen in figure

Fig. 1.16B,D. In other words, the effective near zone of the nanoantenna is maximal in the superdirective

regime.

Usually, high directivity of plasmonic nanoantennas is achieved by the excitation of higher

electrical multipole moments in plasmonic nanoparticles [83, 113, 114] or for core-shell resonators

consisting of a plasmonic material and a hypothetic metamaterial which would demonstrate the

extreme material properties in the nanoscale [115]. Although, the values of directivity achieved for such

nanoantennas do not allow superdirectivity, these studies stress the importance of higher multipoles

for the antenna directivity.

Next, we demonstrate how to find multipole modes excited in the all-dielectric superdirective

nanoantenna which are responsible for its enhanced directivity. We expand the exactly simulated

internal field, producing the polarization currents in the nanoparticle, into multipole moments following

to [116]. The expansion is a series of vector spherical harmonics with the coefficients aE(l, m) and

aM(l, m), which characterize the electrical and magnetic multipole moments [116]:

19

aE(l, m) =4πk2

i√

l(l + 1)

∫

Y ∗lm

[

ρ∂

∂r[rjl(kr)] +

ik

c(r · j)jl(kr)

]

d3x,

aM(l, m) =4πk2

i√

l(l + 1)

∫

Y ∗lmdiv

(

r× j

c

)

jl(kr)d3x, (1.7)

where ρ = 1/(4π)div(E) and j = c/(4π)(rot(H) + ikE) are densities of the total electrical charges and

currents that can be easily expressed through the internal electric E and magnetic H fields of the sphere,

Ylm are the spherical harmonics of the orders (l > 0 and 0 ≥ |m| ≤ l), k = 2π/λ, jl(kr) are the l-order

spherical Bessel function and c is the speed of light. Coefficients aE(l, m) and aM(l, m) determine the

electric and magnetic mutipole moments, namely dipole at l = 1, quadrupole at l = 2, octupole at

l = 3 etc.

The multipole coefficients determine not only the mode structure of the internal field but also the

angular distribution of the radiation. In particular, in the far field zone electric and magnetic fields of

l-order multipole depend on the distance r as [116] ∼ (−1)i+1 exp(ikr)kr

and expression for the angular

distribution of the radiation power can be written as follows:

dP (θ, ϕ)

dΩ=

c

8πk2

∣

∣

∣

∣

∣

∑

l,m

(−i)l+1[aE(l, m)Xlm × n+ aM(l, m)Xlm]

∣

∣

∣

∣

∣

2

,

Xlm(θ, ϕ) =1

√

l(l + 1)

A−l,mYl,m+1 + A+

l,mYl,m−1

−iA−l,mYl,m+1 + iA+

l,mYl,m−1

mYl,m

, (1.8)

where A±l,m = (1/2)

√

(l ±m)(l ∓m+ 1), dΩ = sin(θ)dθdϕ is the solid angle element in spherical

coordinates and n - unit vector of the observation point. All coefficients aE(l, m) and aM(l, m) give

Fig. 1.17 – Absolute values and phases of (A) electric and (B) magnetic multipole moments thatprovide the main contribution of the radiation of all-dielectric superdirective optical nanoantenna at

the wavelength 455 nm. Multipole coefficients providing the largest contribution to the antennadirection are highlighted by red circles.

20

the same contribution to the radiation, if they have the same values. Since higher-order multipoles for

optically small systems have usually negligibly small amplitudes compared to aE(1, m) and aM (1, m),

they are, as a rule, not considered.

The amplitudes of multipole moments, are found by using the expressions (1.7) for electric and

magnetic fields distribution Fig. 1.16A-D are shown in Fig. 1.17, where we observe strong excitation of

aE(1, 0), aM(1, 1), aM(1,−1), aM(2, 2), aM (2,−2), aM(3, 3), aM(3,−3), aM (4, 2), aM(4,−2), aM(4, 4)

and aM(4,−4). These multipole moments determine the angular pattern of the antenna. All other

ones give a negligible contribution. Absolute values of all magnetic moments are larger than those of

the electric moments in the corresponding multipole orders, and the effective spectrum of magnetic

multipoles is also broader than the one of the electric moments. Thus, the operation of the antenna

is mainly determined by the magnetic multipole response. Absolute values of multipole coefficients

aM(l,±|m|) of the same order l are practically equivalent. However, the phase of some coefficients are

different. Therefore, the modes with +|m| and −|m| form a strong anisotropy of the forward–backward

directions that results in the unidirectional radiation.

We have performed the transformation of multipole coefficients into an angular distribution of

radiation in accordance to (1.8) by using distribution of the electric and magnetic fields Fig. 1.16A-D

and determined the relative contribution of each order l. Fig. 1.16E shows how the directivity grows

versus the spectrum of multipoles with equivalent amplitudes. The right panel of Fig. 1.16E nearly

corresponds to the inset in Fig. 1.15 that fits to the results shown in Fig. 1.16E.

Generally, the superdirectivity effect is accompanied by a significant increase of the effective near

field zone of the antenna compared to the one of a point dipole for which the near zone radius is equal

to λ/2π. In the optical frequency range this effect is especially important, considering the crucial role

of the near fields at the nanoscale.

Usually, the superdirectivity regime corresponds to a strong increase of dissipative losses [80].

Radiation efficiency of the nanoantenna is determined by ηrad = Prad/Pin, where Pin is the accepted

input power of the nanoantenna. However, the multipole moments excited in our nanoantenna are

mainly of magnetic type that leads to a strong increase of the near magnetic field that dominates

over the electric one. Since the dielectric material does not dissipate the magnetic energy, the effect

of superdirectivity does not lead to a so large increase of losses in our nanoantenna as it would be in

the case of dominating electric multipoles. However, since the electric near field is nonzero the losses

are not negligible. At wavelengths 440-460 nm (blue light) the directivity achieves 10 but the radiation

efficiency is less than 0.1 (see [Fig. 1.18)]. This is because silicon has very high losses in this range [79].

Peak of directivity is shifted to longer wavelengths with the increase of the nanoantenna size. For

the design parameters corresponding to the operation wavelength 630 nm (red light) the calculated

value of radiation efficiency is as high as 0.5, with nearly same directivity close to 10. In the infrared

range, there are high dielectric permittivity materials with even lower losses. In principle, the proposed

superdirectivity effect is not achieved by price of increased losses, and this is an important advantage

compared to known superdirective radio-frequency antenna arrays [80] and compared to their possible

optical analogues – arrays of plasmonic nanoantennas.

21

(ii) Steering of light at the nanoscale

Here we examine the response of the nanoantenna to subwavelength displacements of the emitter.

Displacement in the plane perpendicular to the axial symmetry of antenna (i.e. along the y axis) leads to

the rotation of the beam without damaging the superdirectivity. Fig.1.19A shows the radiation patterns

of the antenna with the source in center (solid line) and the rotation of the beam for the 20 nm left/right

offset (dashed lines). Shifting of the source in the right side leads to the rotation of pattern to the left,

and vice versa. The angle of the beam rotation is equal to 20 degrees, that is essential and available

to experimental observations. The result depends on the geometry of the notch. For a hemispherical

notch, the dependence of the rotation angle on the displacement is presented in Fig.1.19B.

To interpret the beam steering effect, we can consider the result of field expansion to electric

and magnetic multipoles, as shown in Fig.1.20. In the case of asymmetrical location (the 20 nm left

offset) of the source in the notch absolute values of aM (l,±|m|) are different. This means that the

mode aM (l,+|m|) is excited more strongly than aM (l,−|m|), or vice versa, that depends on direction

of displacement. The effect of superdirectivity remains even with an offset of the source until to the

edge of the notch. Small displacements of the source along x and z do not lead to the rotation of the

pattern.

Instead of the movement of a single quantum dot one we can have the emission of two or more

quantum dots located near the edges of the notch. In this case, the dynamics of their spontaneous

decay will be well displayed in the angular distribution of the radiation. This can be useful for quantum

information processing and for biomedical applications.

Beam steering effect described above is similar to the effect of beam rotation in hyperlens [117–

119], where the displacement of a point-like source leads to a change of the angular distribution of the

radiation power. However, in our case, the nanoantenna has subwavelength dimensions and therefore it

can be neither classified as a hyperlens nor as a micro-spherical dielectric nanoscope [104,105], moreover

it is not an analogue of solid immersion micro-lenses [108–111], which are characterized by the size

1-5 µm in the same frequency range. These lens has a subwavelength resolving power due to the large

geometric aperture but the value of normalized effective aperture is Sn ≃ 1. Our study demonstrates

that the sub-wavelength system, with small compared to the wavelength geometric aperture can have

Fig. 1.18 – Dependence of directivity (A) and radiation efficiency (B) on the size of nanoantenna.Here, the blue solid lines corresponds to the geometry – Rs = 90 nm, Rn = 40 nm, the green dashedcurves – Rs = 120 nm, Rn = 55 nm and red point curves – Rs = 150 nm, Rn = 65 nm. Growth of the

nanoantenna efficiency due to the reduction of dissipative losses in silicon with increasing ofwavelength.

22

Fig. 1.19 – The rotation effect of the main beam radiation pattern, with subwavelength displacementof emitter inside the notch. (A) The radiation patterns of the antenna with the source in center (solidline) and the rotation of the beam radiation pattern for the 20 nm left/right offset (dashed lines). (B)

Dependence of the rotation angle on the source offset.

both high directing and resolving power because of a strong increase of the effective aperture compared

to the geometrical one.

(iii) Experimental verification of superdirective optical nanoantenna

We have confirmed both predicted effects studying the similar problem for the microwave range.

Therefore, we have scaled up the nanoantenna as above to low frequencies. Instead of Si we employ

MgO-TiO2 ceramic [46] characterized at microwaves by a dispersion-less dielectric constant 16 and

dielectric loss factor of 1.12·10−4. We have used the sphere of radius Rs = 5 mm and applied a small

wire dipole [80] excited by a coaxial cable as shown in Fig. 1.21A,B. The size of the hemispherical notch

is approximately equal to Rn = 2 mm. Antenna properties have been studied in an anechoic chamber

Fig. 1.21C.

Fig. 1.20 – Absolute values and phases of (A) electric and (B) magnetic multipole moments thatprovide the main contribution to the radiation of all-dielectric superdirective optical nanoantenna incase of asymmetrical location of source at the wavelength 455 nm. Coefficients that give the largest

contribution to the antenna directivity are highlighted by red circles.

23

Fig. 1.21 – Photographs of (A) top view and (B) perspective view of a notched all-dielectricmicrowave antenna. Image of (C) the experimental setup for measuring of power patterns.

Experimental (i) and numerical (ii) radiation patterns of the antenna in both E- and H-planes at thefrequency 16.8 GHz. The crosses and circles correspond to the experimental data. Experimental (iii)and numerical (iv) demonstration of beam steering effect, displacement of dipole is equal 0.5 mm.

The results of the experimental investigations and numerical simulations of the pattern in both

E- and H-planes are summarized in Figs. 1.21i,ii. Radiation patterns in both planes are narrow beams

with a lobe angle about 35. Experimentally obtained coefficients of the directivity in both E- and

H-planes are equal to 5.9 and 8.4, respectively (theoretical predictions for them were respectively equal

6.8 and 8.1). Our experimental data are in a good agreement with the numerical results except a small

difference for the E plane, that can be explained by the imperfect symmetry of the emitter. Note, that

the observed directivity is close to that of an all-dielectric Yagi-Uda antenna with maximum size of

2λ [46]. The maximum size of our experimental antenna is closed to λ/2.5. Thus, our experiment clearly

demonstrates the superdirective effect.

Experimental and numerical demonstration of the beam steering effect are presented in

Figs. 1.21iii,iv. For the chosen geometry of antenna, displacement of source by 0.5 mm leads to a

beam rotation of about 10. Note that the ratio of λ = 18.7 mm to value of the source displacement 0.5

mm is equal to 37. Therefore the beam steering effect observed at subwavelength source displacement.

Finally, we consider the question of dielectric superdirective antenna matching with coaxial cable.

Despite that length of the wire dipole is close to λ/10, dielectric superdirective antenna is well matched

with the coaxial cable in the operating frequency range. The antenna matching is explained by the

strong coupling of the wire dipole with the excited modes of notched dielectric particle and is not

related to the dissipative losses in the superdirectivity regime. For this reason, we have not used

additional matching devices (e.g. "balun").

Though the concept of the superdirectivity of high-refractive index dielectric particles with notch

has now only been proven in GHz spectral range there is a hope that it can be transferred into the

visible and near-IR spectrum in the nearest future. Recently we have experimentally demonstrated

that it is possible to engineer resonant modes of spherical nanoresonators using a combined approach

24

of laser-induced transfer to generate almost perfect spherical nanoparticles and helium ion beam milling

to structure their surface with sub-5nm resolution [120]. This novel approach can become a suitable

candidate for realizing all-dielectric superdirective nanoantennas.

Conclusion

We propose a new type of highly efficient Yagi-Uda nanoantenna and introduced a novel concept

of superdirective nanoantennas based on silicon nanoparticles. In addition to the electric response,

this silicon nanoantennas exhibit very strong magnetic resonances at the nanoscale. Both types of

nanoantennas are studied analytically, numerically and experimentally. For superdirective nanoantennas

we also predict the effect of the beam steering at the nanoscale characterized by a subwavelength

sensitivity of the beam radiation direction to the source position.

The unique optical properties and low losses make dielectric nanoparticles perfect candidates

for a design of high-performance nanoantennas, low-loss metamaterials, and other novel all-dielectric

nanophotonic devices. The key to such novel functionalities of high-index dielectric nanophotonic

elements is the ability of subwavelength dielectric nanoparticles to support simultaneously both electric

and magnetic resonances, which can be controlled independently for particles of non spherical forms.

25

References

[1] P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Advances in Optics andPhotonics 1, pp. 438–483, 2009.

[2] L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, pp. 83–90, 2011.

[3] A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst,“Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, pp. 930–933,2010.

[4] T. Taminiau, F. Stefani, F. Segerink, and N. V. Hulst, “Optical antennas direct single-moleculeemission,” Nat. Photonics. 2, pp. 234–237, 2008.

[5] L. Novotny, “Optical antennas tuned to pitch,” Nature 455, p. 887, 2008.

[6] S. He, Y. Cui, Y. Ye, P. Zhang, and Y. Jin, “Optical nanoantennas and metamaterials,” MaterialsToday 12, p. 16, 2009.

[7] L. Novotny and B. Hecht, Principles of Nano-Optics, Cambridge University Press, 2006.

[8] A. Krasnok, I. Maksymov, A. Denisyuk, P. Belov, A. Miroshnichenko, C. Simovski, andY. Kivshar, “Optical nanoantennas,” Phys.-Usp. 56, p. 539, 2013.

[9] A. Krasnok and P. Belov, Optical nanonatennas, LAP LAMBERT Academic Publishing, 2013.

[10] M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active opticalantennas,” Science 332, pp. 702–704, 2011.

[11] M. F. Garcia-Parajo, “Optical antennas focus in on biology,” Nature Photonics 2, pp. 201–203,2008.

[12] A. Alu and N. Engheta, “Wireless at the nanoscale: Optical interconnects using matchednanoantennas,” Phys. Rev. Lett. 104, p. 213902, 2010.

[13] B. J. Roxworthy, K. D. Ko, A. Kumar, K. H. Fung, E. K. C. Chow, G. L. Liu, N. X. Fang,and K. C. Toussaint, “Application of plasmonic bowtie nanoantenna arrays for optical trapping,stacking, and sorting,” Nano Lett. 12, pp. 796–801, 2012.

[14] A. Andryieuski, R. Malureanu, G. Biagi, T. Holmgaard, and A. Lavrinenko, “Compact dipolenanoantenna coupler to plasmonic slot waveguide,” Opt. Lett. 37, pp. 1124–1126, 2012.

[15] B. Khlebtsov, A. Melnikov, V. Zharov, and N. Khlebtsov, “Absorption and scattering of light by adimer of metal nanospheres: comparison of dipole and multipole approaches,” Nanotechnology 17,p. 1437, 2006.

[16] F. Gonzalez and G. Boreman, “Comparison of dipole, bowtie, spiral and log-periodic ir antennas,”Infrared Phys. Tech. 46, pp. 418–428, 2005.

[17] Z. Fang, L. Fan, C. Lin, D. Zhang, A. J. Meixner, and X. Zhu, “Plasmonic coupling of bow tieantennas with ag nanowire,” Nano Lett. 11, 2011.

[18] H. Guo, T. P. Meyrath, T. Zentgraf, N. Liu, L. Fu, H. Schweizer, and H. Giessen, “Opticalresonances of bowtie slot antennas and their geometry and material dependence,” Opt. Express 16,pp. 7756–7766, 2008.

26

[19] N. A. Hatab, C.-H. Hsueh, A. L. Gaddis, S. T. Retterer, J.-H. Li, G. Eres, Z. Zhang, andB. Gu, “Free-standing optical gold bowtie nanoantenna with variable gap size for enhanced ramanspectroscopy,” Nano Lett. 10, 2010.

[20] A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Phot. 3, pp. 654–657, 2009.

[21] K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint,“Nonlinear optical response from arrays of au bowtie nanoantennas,” Nano Lett. 11, 2011.

[22] S. Sederberg and A. Y. Elezzabi, “Nanoscale plasmonic contour bowtie antenna operating in themid-infrared,” Opt. Express 19, pp. 15532–15537, 2011.

[23] J. Y. Suh, M. D. Huntington, C. H. Kim, W. Zhou, M. R. Wasielewski, and T. W. Odom,“Extraordinary nonlinear absorption in 3d bowtie nanoantennas,” Nano Lett. 12, 2012.

[24] Z. Zhang, A. Weber-Bargioni, S. W. Wu, S. Dhuey, S. Cabrini, and P. J. Schuck, “Manipulatingnanoscale light fields with the asymmetric bowtie nano-colorsorter,” Nano Lett. 9, pp. 4505–4509,2009.

[25] A. Alu and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of opticalnanoantennas,” PRL 101, p. 043901, 2008.

[26] A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuitloads,” Nat. Phot. 2, pp. 307–310, 2008.

[27] T. Coenen, E. J. R. Vesseur, A. Polman, and A. F. Koenderink, “Directional emission fromplasmonic yagi-uda antennas probed by angle-resolved cathodoluminescence spectroscopy,” NanoLett. 11, pp. 3779–3784, 2011.

[28] J. Dorfmuller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen,“Near-field dynamics of optical yagi-uda nanoantennas,” Nano Lett. 11, pp. 2819–2824, 2011.

[29] H. F. Hofmann, T. Kosako, and Y. Kadoya New Journal of Physics 9, p. 217, 2007.

[30] G. Lerosey, “Nano-optics: Yagi–uda antenna shines bright,” Nat. Phot. 4, pp. 267–268, 2010.

[31] J. Li, A. Salandrino, and N. Engheta, “Optical spectrometer at the nanoscale using optical yagi-uda nanoantennas,” Phys. Rev. B 79, p. 195104, 2009.

[32] S. V. Lobanov, T. Weiss, D. Dregely, H. Giessen, N. A. Gippius, and S. G. Tikhodeev, “Emissionproperties of an oscillating point dipole from a gold yagi-uda nanoantenna array,” Phys. Rev.B 85, p. 155137, 2012.

[33] I. S. Maksymov, I. Staude, A. E. Miroshnichenko, and Y. S. Kivshar, “Optical yagi-udananoantennas,” Nanophotonics 1, pp. 65–81, 2012.

[34] I. S. Maksymov, A. E. Miroshnichenko, and Y. S. Kivshar, “Actively tunable bistable opticalyagi-uda nanoantenna,” Opics Express 20, pp. 8929–8938, 2012.

[35] T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emissionof single emitters by a nano-optical yagi-uda antenna.,” Opt. Express 16, pp. 16858–16866, 2008.

[36] A. E. Krasnok, C. R. Simovski, P. A. Belov, and Y. S. Kivshar, “Superdirective dielectricnanoantenna,” Nanoscale 6, pp. 7354–7361, 2014.

[37] A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric opticalnanoantennas,” Optics Express 20, p. 20599, 2012.

[38] V. Dzyuba, A. Krasnok, and Y. Kulchin, “A model of nonlinear optical transmittance for insulatornanocomposites,” Semiconductors 45, pp. 295–301, 2011.

[39] V. P. Dzyuba, A. E. Krasnok, and Y. N. Kul’chin, “Nonlinear refractive index of dielectricnanocomposites in weak optical fields,” Technical Physics Letters 36, pp. 973–977, 2010.

27

[40] A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric opticalnanoantennas,” AIP Conf. Proc. 1475, pp. 22–24, 2012.

[41] A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectricnanoantennas,” Proc. of SPIE 8806, p. 880626, 2013.

[42] R. E. Noskov, A. E. Krasnok, and Y. S. Kivshar, “Nonlinear metal-dielectric nanoantennas forlight switching and routing,” New Journal of Physics 14, p. 093005, 2012.

[43] D. S. Filonov, A. P. Slobozhanyuk, A. E. Krasnok, P. A. Belov, E. A. Nenasheva, B. Hopkins,A. E. Miroshnichenko, and Y. S. Kivshar, “Near-field mapping of fano resonances in all-dielectricoligomers,” Appl. Phys. Lett. 104, p. 021104, 2014.

[44] A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “Huygens optical elementsand yagi–uda nanoantennas based on dielectric nanoparticles,” JETP Lett. 94, p. 635, 2011.

[45] A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric opticalnanoantennas,” Opt. Express 20, pp. 20599–20604, 2012.

[46] D. S. Filonov, A. E. Krasnok, A. P. Slobozhanyuk, P. V. Kapitanova, E. A. Nenasheva, Y. S.Kivshar, and P. A. Belov, “Experimental verification of the concept of all-dielectric nanoantennas,”Appl. Phys. Lett. 100, p. 201113, 2012.

[47] A. Kuznetsov, A. Miroshnichenko, Y. Fu, J. Zhang, and B. Lukyanchuk, “Magnetic light,” Sci.Rep. 2, p. 492, 2012.

[48] L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media.,Butterworth-Heinemann, Oxford, 2002.

[49] V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photon. 1, pp. 41–47, 2007.

[50] N. I. Zheludev, “The road ahead for metamaterials,” Science 328, pp. 582–583, 2010.

[51] C. M. Soukoulis and M. Wegener Science 330, pp. 1633–1634, 2010.

[52] A. Boltasseva and H. A. Atwater, “Low-loss plasmonic metamaterials,” Science 331, pp. 290–291,2011.

[53] C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the developmentof three-dimensional photonic metamaterials,” Nature Photon. 5, pp. 523–530, 2011.

[54] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors andenhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, pp. 2075–2084, 1999.

[55] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite mediumwith simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, pp. 4184–4187,2000.

[56] R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index ofrefraction,” Science 292, 2001.

[57] D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivityand permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65,p. 195104, 2002.

[58] U. Leonhardt, “Optical conformal mapping,” Science 312, pp. 1777–1780, 2006.

[59] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312,pp. 1780–1782, 2006.

[60] J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, pp. 3966–3969,2000.

[61] T. J. Yen, T. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, andX. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 2004.

28

[62] W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric andmagnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, p. 107401, 2006.

[63] S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic responseof metamaterials at 100 terahertz,” Science 306, 2004.

[64] C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny,and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,”Phys. Rev. Lett. 95, p. 203901, 2005.

[65] N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonicmetamaterials at optical frequencies,” Nature Mater. 7, 2008.

[66] C. M. Soukoulis, T. Koschny, J. Zhou, M. Kafesaki, and E. N. Economou, “Magnetic response ofsplit ring resonators at terahertz frequencies,” Phys. Stat. Sol. B 244, pp. 1181–1187, 2007.

[67] Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials.,”Mater. Today 12, 2009.

[68] L. Cao, P. Fan, E. S. Barnard, A. M. Brown, and M. L. Brongersma, “Tuning the color of siliconnanostructures,” Nano Lett. 10, pp. 2649–2654, 2010.

[69] “Optical response features of si-nanoparticle arrays,” Phys. Rev. B 82, p. 045404, 2010.

[70] A. Garcia-Etxarri, R. Gomez-Medina, L. S. Froufe-Perez, C. Lopez, L. Chantada, F. Scheffold,J. Aizpurua, M. Nieto-Vesperinas, and J. J. Saenz, “Strong magnetic response of submicron siliconparticles in the infrared,” Opt. Express 19, pp. 4815–4826, 2011.

[71] A. V. Kabashin and M. Meunier, “Synthesis of colloidal nanoparticles during femtosecond laserablation of gold in water,” J. Appl. Phys. 94, 2003.

[72] C. Bohren and D. Huffman, Absorption and scattering of light by small particles, New York :Wiley, 1998.

[73] A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, andB. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in thevisible region,” Nano Lett. 12, p. 3749, 2012.

[74] Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Lukyanchuk, “Directionalvisible light scattering by silicon nanoparticles,” Nat. Comm. 4, p. 1527, 2013.

[75] M. Kerker, D.-S. Wang, and C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J.Opt. Soc. Am. 73, pp. 765–767, Jun 1983.

[76] J. Geffrin, “Magnetic and electric coherence in forward- and back-scattered electromagnetic wavesby a single dielectric subwavelength sphere,” Nat. Comm. 3, p. 1, 2012.

[77] S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zerooptical backscattering from single nanoparticles,” Nano Letters 13(4), pp. 1806–1809, 2013.

[78] M. K. Schmidt, R. Esteban, J. J. S?enz, I. Su?rez-Lacalle, S. Mackowski, and J. Aizpurua,“Dielectric antennas - a suitable platform for controlling magnetic dipolar emission,” OpticsExpress 20, pp. 13636–13650, 2012.

[79] E. Palik, Handbook of Optical Constant of Solids, San Diego, Academic, 1985.

[80] C. Balanis, Antenna theory : analysis and design, New York ; Brisbane : J. Wiley, 1982.

[81] “Optically induced interaction of magnetic moments in hybrid metamaterials,” ASC Nano 6,pp. 837–842, 2012.

[82] O. Merchiers, F. Moreno, F. Gonzalez, and J. M. Saiz, “Light scattering by an ensemble ofinteracting dipolar particles with both electric and magnetic polarizabilities,” Phys. Rev. A 76,p. 043834, 2007.

29

[83] B. Rolly, B. Stout, S. Bidault, and N. Bonod Opt. Lett. 36, pp. 3368–3370, 2011.

[84] L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, pp. 83–90, 2011.

[85] H. Chew, “Transition rates of atoms near spherical surfaces,” J. Chern. Phys. 87, p. 1355, 1987.

[86] Y. lin Xu and B. A. S. Gustafson, “A generalized multiparticle mie-solution: further experimentalverification,” J. Quant. Spectrosc. Radiat. Transfer 70, pp. 395–419, 2001.

[87] E. Dulkeith, M. Ringler, T. A. Klar, J. Feldmann, A. M. Javier, and W. J. Parak, “Goldnanoparticles quench fluorescence by phase induced radiative rate suppression,” Nano Lett. 5,pp. 585–589, 2005.

[88] A. Kanareykin, W. Gai, J. G. Power, E. Nenasheva, and A. Altmark, “Transformer ratioenhancement experiment,” in Proceedings Particle Accelerator Conference, pp. 1894–1896, 2003.

[89] N. Halas, “Connecting the dots: Reinventing optics for nanoscale dimensions,” PNAS 106, p. 3643,2010.

[90] P. Biagioni, J. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep.Prog. Phys. 75, p. 024402, 2012.

[91] D. Solis, J. Taboada, F. Obelleiro, and L. Landesa, “Optimization of an optical wireless nanolinkusing directive nanoantennas,” Optics Express 21, p. 2369, 2013.

[92] D. Dregely, R. Taubert, J. Dorfmuller, R. Vogelgesang, K. Kern, and H. Giessen, “3d opticalyagi−uda nanoantenna array,” Nat. Comm. 2, pp. 1–7, 2011.

[93] Y. G. Liu, W. C. H. Choy, W. E. I. Sha, and W. C. Chew, “Unidirectional and wavelength-selectivephotonic sphere-array nanoantennas,” Optics Lett. 37, p. 2112, 2012.

[94] A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultradirectional and enhanced radiative emission,” ACS Nano 4, pp. 3390–3396, 2010.

[95] A. Ludwig, C. Sarris, and G. Eleftheriades, “Metascreen-based superdirective antenna in theoptical frequency regime,” Phys. Rev. Lett. 109, p. 223901, 2012.

[96] P. K. Jain and M. A. El-Sayed, “Plasmonic coupling in noble metal nanostructures,” ChemicalPhysics Letters 487, 2010.

[97] S. R. K. Rodriguez, S. Murai, M. A. Verschuuren, and J. G. Rivas, “Light-emitting waveguide-plasmon polaritons,” Phys. Rev. Lett. 109, p. 166803, 2012.

[98] B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magneticand electric dipolar resonant particles,” Optics Exp. 20, p. 20376, 2012.

[99] R. Hansen, Electrically small, superdirective, and superconducting antennas, Wiley-Interscience,2006.

[100] R. Hansen and R. Collin, Small Antenna Handbook, John Wiley and Sons Ltd, 2011.

[101] S. Boriskina, T. Benson, P. Sewell, and A. Nosich, “Directional emission, increased free spectralrange and mode q-factors in 2-d wavelength-scale optical microcavity structures,” IEEE J. Select.Topics Quantum Electron. 12, pp. 1175–1182, 2006.

[102] Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura,M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highlyunidirectional laser action,” PNAS 107, p. 22407, 2010.

[103] M. O. Scully, “Collimated unidirectional laser beams from notched elliptical resonators,”PNAS 107, p. 22367, 2010.

[104] J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S.Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, “Near-field focusing andmagnification through self-assembled nanoscale spherical lenses,” Nature 460, p. 498, 2009.

30

[105] Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Opticalvirtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Comm. 2, p. 1,2011.

[106] L. Gabrielli and M. Lipson, “Integrated luneburg lens via ultra-strong index gradient on silicon,”Opt. Expr. 19, p. 20122, 2011.

[107] A. Falco, S. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Expr. 19, p. 5156,2011.

[108] D. Gerard, J. Wenger, A. Devilez, D. Gachet, B. Stout, N. Bonod, E. Popov, and H. Rigneault,“Strong electromagnetic confinement near dielectric microspheres to enhance single-moleculefluorescence,” Opt. Expr. 16, p. 15297, 2008.

[109] J. Schwartz, S. Stavrakis, and S. Quake, “Colloidal lenses allow high-temperature single-moleculeimaging and improve fluorophore photostability,” Nat Nanotechnol. 5, p. 127, 2010.

[110] L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, and R. Hanson, “High-fidelityprojective read-out of a solid-state spin quantum register,” Nature 477, p. 574, 2011.

[111] P. Siyushev, F. Kaiser, V. Jacques, I. Gerhardt, S. Bischof, H. Fedder, J. Dodson, M. Markham,D. Twitchen, F. Jelezko, and J. Wrachtrup, “Monolithic diamond optics for single photondetection,” Appl. Phys. Lett. 97, p. 241902, 2010.

[112] V. Klimov, Nanoplasmonics, Pan Stanford Publishing, 2011.

[113] T. Pakizeh and M. Kall, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9,p. 2343, 2009.

[114] S. A. Lavasani and T. Pakizeh, “Color-switched directional ultracompact optical nanoantennas,”Opt. Lett. 29, p. 1361, 2012.

[115] A. Alu and N. Engheta, “Enhanced directivity from subwavelength infrared/optical nano-antennas loaded with plasmonic materials or metamaterials,” IEEE Trans. on Antennas andPropagation 55, p. 3027, 2007.

[116] J. Jackson, Classical Electrodynamics, New York : Wiley, 1998.

[117] Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, p. 1686, 2007.

[118] Z. Jacob, L. Alekseyev, and E. Narimanov, “Optical hyperlens: Far-field imaging beyond thediffraction limit,” Opt. Expr. 14, p. 8247, 2006.

[119] D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat.Comm. 3, p. 1, 2012.

[120] A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, V. Viswanathan, M. Rahmani, V. Valuckas,Z. Y. Pan, Y. Kivshar, D. S. Pickard, and B. Luk’yanchuk, “Split-ball resonator as a three-dimensional analogue of planar split-rings,” Nature Communications 5, p. 3104, 2013.

31